Notre Dame Journal of Formal Logic

Halldén Completeness for Relevant Modal Logics

Takahiro Seki

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Halldén completeness closely resembles the relevance property. To prove Halldén completeness in terms of Kripke-style semantics, the van Benthem–Humberstone theorem is often used. In relevant modal logics, the Halldén completeness of Meyer–Fuhrmann logics has been obtained using the van Benthem–Humberstone theorem. However, there remain a number of Halldén-incomplete relevant modal logics. This paper discusses the Halldén completeness of a wider class of relevant modal logics, namely, those with some Sahlqvist axioms.

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Notre Dame J. Formal Logic, Volume 56, Number 2 (2015), 333-350.

First available in Project Euclid: 17 April 2015

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Zentralblatt MATH identifier

Primary: 03B45: Modal logic (including the logic of norms) {For knowledge and belief, see 03B42; for temporal logic, see 03B44; for provability logic, see also 03F45}
Secondary: 03B47: Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) {For proof-theoretic aspects see 03F52}

Halldén completeness relevant modal logics Routley–Meyer semantics van Benthem–Humberstone theorem Sahlqvist formulas


Seki, Takahiro. Halldén Completeness for Relevant Modal Logics. Notre Dame J. Formal Logic 56 (2015), no. 2, 333--350. doi:10.1215/00294527-2864334.

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